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July 20, 2026The Electronic Journal of CombinatoricsOpen Access

RSK Linear Operators and the Vershik-Kerov-Logan-Shepp Curve

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Authors

DPDuy PhanUniversity of Illinois Urbana-ChampaignDXDavid XiaUniversity of Illinois Urbana-Champaign

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Overview

Study demonstrates block diagonal nature of RSK operators and identifies zero entries via Probabilistic Analysis.

Key Points

  • The aim is to establish the conjecture about the vanishing of diagonal entries in RSK's linear operator on matrices.
  • Analyzed RSK correspondence as a linear operator on the coordinate ring of matrices.
  • Identified zeros in a specialized block related to Schensted insertion interactions.
  • Applied probabilistic analysis using the Vershik-Kerov-Logan-Shepp Limit Shape Theorem.
  • Confirmed that most diagonal entries in a special block vanish.
  • Established a relationship between zeros and Schensted insertion interactions.
  • Validated the conjecture using probabilistic approaches.

Cite This Study

Phan et al. (2026) studied this question.

synapsesocial.com/papers/6a5db9da8bd453d3397ab2b7https://doi.org/10.37236/14670
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1RSK as a linear operator2026
  2. 2Fluctuations of Schensted row insertion2026
  3. 3Representations from matrix varieties, and filtered RSK2024
  4. 4An extended generalization of RSK via the combinatorics of type $A$ quiver representations2024
  5. 5Oppenheim-Schur's inequality and RKHS2024